To alleviate these limitations, as illustrated in Fig. REF , we introduce Volume Embedding Module (VEM) to not only reduce the computation by effectively decreasing the number of tokens, but also inject some convolutional inductive bias [1]} to help the subsequent transformer-based model to improve the ability of learning interactions among the hypercorrelation.
Concretely, we sequentially reduce support and query spatial dimensions by applying 4D spatial max-pooling, overlapping 4D convolutions, RELU, and Group Normalization (GN), where we project the multi-level similarity vector at each 4D position, i.e., projecting a vector size of \(|\mathcal {L}_p|\)  to a arbitrary fixed dimension denoted as \(D\) . Considering receptive fields of VEM as 4D window size, i.e., \(m\times m\times m\times m\) , we build a tensor \(\mathcal {M} \in \mathbb {R}^{\hat{h}_{q}\times \hat{w}_{q} \times \hat{h}_{s} \times \hat{w}_{s} \times D}\) , where \(\hat{h}\)  and \(\hat{w}\)  are the processed sizes. Note that different size of output can be made for source and target spatial dimensions by varying the hyperparameters.
